help me? ocr mei a level vectorsWatch
im usually okay at vectors but i dont understand 7ii
i get you have to find the angle between the normal vector but it then says horizontal plane, why is this 0 0 1
thanks in advance
The ground level is represented here as the plane 0x+0y+z=0 (same as z=0). To find the normal vector you always take the coefficients of the x,y and z. The coefficient of x is 0, y is 0 and z is 1 so we get the normal vector to this horizontal plane as (0,0,1)
It lies on the x axis but that doesn't make x the horizontal plane. If you think about all the points on the plane, x and y are always changing as you move around the plane but z is always 0 at all points on that plane so the plane has to be z=0.
Yes the ground level is 0 for z but the normal vector has to be 0,0,1 as it is normal to the plane
so its the normal vector with k? k is the coordinate on d so can it be worked out from there